Affinity Matrix Learning through Subspace Clustering for Tolling Zone Definition

Congestion pricing is an aspect of traffic management that endeavours to alter travelers’ decision-making with regards to departure time, route selection, mode choice, trip cancellation. In this paper, we propose the use of subspace clustering, as an innovative approach for defining sets of tolling zones, meant to be used in distance-based tolling implementations. We propose a new variant of Sparse Subspace Clustering by Orthogonal Matching Pursuit (SSCOMP) for learning the self-representation-based affinity matrix. Affinity Propagation clustering is applied on said affinity matrix to derive a tolling zone definition. We compare the proposed tolling zone definition approach with OPTICS, a hierarchical density-based clustering method. Travel speed indices (TSI) are used for the dataset used to perform this new variant of subspace clustering. Clustering results are used by a distance-based tolling optimization framework to evalaute network performance. Results from a Boston CBD network test case show that subspace clustering can produce tolling zone definitions with positive impact on distance-based toll optimization and overall network performance.